A Study On Phase Field Method For Martensitic Transformation Of Superelastic NiTi Shape Memory Alloys

NiTi shape memory alloys(SMAs)have unique shape memory effect(SME)and superelasticity(SE),as well as other excellent mechanical properties such as high strength,high damping capacity and wear-resistant,thus have become the most important and valuable metallic intelligent materials,and also have been increasingly used as structural materials.They have received increasing attention from scientists and engineers in the past several decades.Notably,recently NiTi SMAs are used in many engineering fields including some important civil structures to realize active,semi-active or intelligent control,due to their unique properties of large recoverable strain,high damping,temperature-dependent elasticity,fatigue-resistantce and corrosion-resistantce etc.It is well known that SME and SE of NiTi alloys originate from martensitic transformation,which has significant influence on physical and mechanical properties of the alloys.To fully utilize the alloy's properties and design NiTi SMA based structures and devices,it is imperative to investigate the microstructural morphology of the alloy during transformation and establish the correlation between the microstructure and the mechanical property.The phase field method as one of the most powerful tools for simulating and predicting the microstructure,has been extensively developed and widely used in the past thirty years;in particular,the past twenty years have seen increasing applications of phase field models in damage analysis of structures and structural topology optimization.However,for the phase field method there are still some serious issues to resolve,such as a large number of variables used in phase field equations,complicated coupling relationship,extremely small simulation scale and large amount of computation,which have significantly limited the wide application of phase field method.Under such circumstances,thus far,the simulation has to be restricted to smaller systems even using the state-of-the-art computer facilities.In this thesis study,the phase field model of martensitic transformation in superelastic NiTi SMA is studied,an improved phase field method is developed by using statistical learning theory-based optimization algorithm,and then a micro-macro constitutive model base on the phase field method for martensitic transformation materials is established and used to study the microstructure of NiTi alloys.The main contents of the present thesis study are as follows.(1)A two-dimensional(2D)simulation model based on the phase field theory is proposed according to continuity theory of crystal martensite transformation.Then,the model is used for the quasi three-dimensional simulation of the B2–R transformation.The simulation results demonstrate that the quasi three-dimensional model can be used to accurately simulate martensitic transformation with three-dimensional shear strain in a two-dimensional plate.(2)An improved phase field method by using statistical learning theory-based optimization algorithm is developed for solving the phase field equations through building simple relationships between key phase field variables and the phase evolution driving force,and using statistical analysis of mass computed data during phase field simulation.Phase field simulation results of growth of R phase and B2–R phase transformation obtained by using the proposed statistical strategy algorithm and using the conventional numerical algorithm are almost the same,which vindicates the algorithm proposed in the present study.The comparison of simulation results obtained by using two simulation algorithms demonstrates that the new approach can potentially lead to an order of magnitude improvement in efficiency for a prescribed accuracy and meanwhile bring about vastly reduced computational time.(3)A phase field model is constructed by introducing a global modification function to study martensitic transformation in a relatively large scale,in which the modification function takes into account the inhomogeneous characteristics of order parameter gradient across the interfacial region.Through adjusting the free energy density and gradient coefficient,while keeping the interfacial energy density unchanged,the interfacial thickness and system size are increased,yet the martensitic transformation features can be comprehensively revealed and depicted.The simulation results demonstrate that the modified phase field model can well aviod the drawbacks such as fast growth rate of martensite,artificial orientation relationship between the variants of martensite,and disordered martensite microstructure in large scale systems.(4)The coupling relationship between the microstructure of NiTi shape memory alloy and its macroscopic mechanical behavior is studied.At the micro scale,the microstructure evolution is simulated by the phase field model correlated with macro-mechanical properties,and then a micro-and macro-scale constitutive model is constructed.In the model,the equivalent elasticity modulus and the equivalent phase transformation strain are obtained based on the microstructure evolution of the NiTi alloy during transformation process,and then the coupling micro-and macro-scale analyses are conducted.Finally,the developed model is used to analyze the loading and unloading process of the NiTi alloy.The results obtained show that the simulation by using the model can well represent the microstructural characteristics of the NiTi alloy,and meanwhile,exhibit the unique superelastic feature of the alloy,which verifies the feasibility and effectiveness of the micro-and macro-scale model developed in this study.